algebra
nounUK /ˈæl.dʒɪ.bɹə/ · US /ˈæl.d͡ʒɪ.bɹə/
Etymology Borrowed from Medieval Latin algebra, from the Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work الْكِتَاب الْمُخْتَصَر فِي حِسَاب الْجَبْر وَالْمُقَابَلَة (al-kitāb al-muḵtaṣar fī ḥisāb al-jabr wa-l-muqābala, “The Compendious Book on Calculation by Completion and Balancing”).
7 senses
- 1Elementary algebra: A system for representing and…
- 2Abstract algebra: A broad field of study in modern…
- 3A universal algebra.
- 4An algebraic structure consisting of a module over a…
- 5A collection of subsets of a given set, such that this…
- 6A system or process (especially one that is complex or…
- 7The surgical treatment of a dislocated or fractured…
Mathematics, Sciences Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber.1551, James A.H. Murray, editor, A New English Dictionary on Historical Principles: Founded Mainly on the Materials Collected by the Philological Society., volume 1, Oxford: Clarendon Press, published 1888, Part 1, page 217:
- Let us conceive, then, of an Algebra in which the symbols x, y, z, &c. admit indifferently of the values 0 and 1, and of these values alone.1854, George Boole, “Signs and their Laws”, in An Investigation of the Laws of Thought, on which are Founded the Mathematical Theories of Logic and Probabilities, London: Walton and Maberly, page 37:
Mathematics, Sciences Capitalized, Sometimes Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
› Any of several objects of study in Algebra
Algebra, Mathematics, Sciences A universal algebra.
Algebra, Mathematics, Sciences An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
Mathematical analysis, Mathematics, Sciences, Set theory A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
Figuratively A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
- Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what?1663, William Clark, edited by William Hugh Logan, Marciano; or, The discovery: A tragi-comedy, Edinburgh: Reprinted for Private Circulation, published 1871, →ISBN, page 13:
Medicine, Sciences Historical, Rare The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- Ne take noon hede to brynge togidere þe parties of þe boon þat is to-broken or dislocate, til viij. daies ben goon in þe wyntir, & v. in þe somer; for þanne it schal make quytture, and be sikir from swellynge; & þanne brynge togidere þe brynkis eiþer þe disiuncture after þe techynge þat schal be seid in þe chapitle of algebra.a1420, The British Museum Additional MS, 12,056, “Wounds complicated by the Dislocation of a Bone”, in Robert von Fleischhacker, editor, Lanfranc's "Science of cirurgie.", London: K. Paul, Trench, Trübner & Co, translation of original by Lanfranc of Milan, published 1894, →ISBN, page 63:
- Algebra is used today by surgeons to mean bone-setting, i.e. the restoration of bones, and the idea of restoration is present in the mathematical context, too.1987, John Newsome Crossley, “Latency”, in The emergence of number, Singapore: World Scientific, →ISBN, Al-Khwarizwi, page 65:
- Derived terms
85 terms
Abelian algebra, abelian algebra, abstract algebra, Albert algebra, algebraism, algebraist, algebraization, algebraize, algebralike, algebra over a field, algebra over a ring, algebrician, algebroid, alternative algebra, anti-algebra, antialgebra, Artin algebra, associative algebra, Azumaya algebra, Banach algebra, bialgebra, Boolean algebra, Borel σ-algebra, central simple algebra, Clifford algebra, coalgebra, cogebra, combinatorial commutative algebra, commutative algebra, composition algebra, De Morgan algebra, dialgebra, division algebra, elementary algebra, F-algebra, finite algebra, free algebra, free Boolean algebra, Grassmann algebra, hard as Chinese algebra, Hecke algebra, Heyting algebra, homological algebra, Hopf algebra, Hurwitz algebra, hyperalgebra, Iwahori-Hecke algebra, Jordan algebra, Kac-Moody algebra, k-algebra, Kleene algebra, Leibniz algebra, Lie algebra, linear algebra, Loday algebra, Maharam algebra, matrix algebra, modern algebra, multialgebra, non-associative algebra, numerical linear algebra, Ockham algebra, polynomial algebra, power-associative algebra, prealgebra, pseudoalgebra, quasibialgebra, quaternion algebra, reduced algebra, semialgebra, shuffle algebra, sigma-algebra, simple algebra, subalgebra, subalgebrae, submultialgebra, superalgebra, superbialgebra, superdialgebra, switching algebra, universal algebra, vector algebra, Weyl algebra, Zinbiel algebra, σ-algebra- Related terms
- algebraic, algebraical, algebraically, algebraist, algorithm